If yt are the observations and zt is the EWMA, show that the following relationships are true.

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If yt are the observations and zt is the EWMA, show that the following relationships are true.
yt: Observation and zt: EWMA
(a)zt − zt−1 = λ(yt − zt−1)
(b) et − (1 − λ)et−1 = yt − yt−1
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